WEBVTT Kind: captions; Language: en 00:00:00.000 --> 00:00:05.000 Let's see, this room today are things like tutorials. 00:00:08.000 --> 00:00:14.000 And Greg asked me to do a tutorial on some of the things about GPS, 00:00:15.000 --> 00:00:21.000 not just GPS in the sense of what do you get when you go down to Key Mart and 00:00:21.000 --> 00:00:27.000 spend 250 bucks, but a little bit of tutorial on how GPS works, 00:00:28.000 --> 00:00:33.001 what it's all about, what are some of these other funny letters that you keep 00:00:33.001 --> 00:00:38.001 hearing about like SA and things like that, what are their attributes, 00:00:40.000 --> 00:00:47.000 to try to have so that the amateurs have a little 00:00:47.000 --> 00:00:52.000 bit better understanding of the system so that we can figure out new and 00:00:52.000 --> 00:00:53.001 interesting things to do with GPS. 00:00:56.000 --> 00:01:00.001 So Greg asked me for a title, and I didn't think very long when I came up with 00:01:00.001 --> 00:01:06.000 the one that appeared in the program of how does it work and why do I care. 00:01:07.000 --> 00:01:10.000 I'm not sure that I'll cover so many why do I cares, 00:01:11.001 --> 00:01:13.001 but there'll at least be a few. 00:01:16.000 --> 00:01:22.000 GPS of course is the global positioning system 00:01:23.000 --> 00:01:30.000 and we have to keep in mind through all of our discussions that GPS was built 00:01:30.000 --> 00:01:35.000 by the Department of Defense for military navigation and some other purposes. 00:01:36.000 --> 00:01:41.001 It is a military system and the military owns it and they have the keys to do 00:01:41.001 --> 00:01:46.001 everything and if they wanna do something, they will do it, even though in many 00:01:46.001 --> 00:01:50.000 cases, it may be a very stupid thing to do. 00:01:50.000 --> 00:01:56.000 In many cases, it may not make sense and in many cases, you will probably, during 00:01:56.000 --> 00:01:59.001 this little talk I'll give, here we make some irreverent 00:01:59.001 --> 00:02:01.001 comments about our military. 00:02:03.001 --> 00:02:08.001 That's okay, but I wanted to stress that. 00:02:11.001 --> 00:02:18.000 Navigation is really the key word in that and the military, 00:02:18.001 --> 00:02:21.000 navigation is a big thing. 00:02:21.001 --> 00:02:27.001 One of the things that I wanna stress to you all here right at the start is that 00:02:27.001 --> 00:02:32.001 navigation and time are very critically linked. 00:02:32.001 --> 00:02:36.000 All of the, when we talk about how GPS work, it's a timing system. 00:02:37.000 --> 00:02:42.000 When we talk about things that we do with GPS, it's one of the interesting 00:02:42.000 --> 00:02:44.000 applications is to distribute time. 00:02:46.001 --> 00:02:53.000 For those of you who are interested in navigation and interested in time, 00:02:53.001 --> 00:02:59.000 an absolute must read book, if you haven't read it, is a book by Davis Sobel. 00:03:00.000 --> 00:03:06.000 She wrote this book called Longitude and it describes 00:03:06.000 --> 00:03:12.001 the navigation problems of the 1700s. 00:03:12.001 --> 00:03:18.001 Now since amateurs are somewhat technically behind our time in terms of some of 00:03:18.001 --> 00:03:21.001 the things that go on, this may show a little of the applications 00:03:21.001 --> 00:03:23.000 of relevant technology. 00:03:23.001 --> 00:03:30.000 Specifically, it tells the story of John Harrison and his attempt to claim the 00:03:30.000 --> 00:03:35.001 prize that would allow ships to navigate into their home harbor safely. 00:03:37.000 --> 00:03:42.001 Tells the story in here of ships that were wrecked because they thought they were 00:03:42.001 --> 00:03:47.000 about ready to steam in home and ended up being 60 miles away. 00:03:49.000 --> 00:03:54.000 And needless to say, the appearance of reefs and rocks and so forth 60 miles 00:03:54.000 --> 00:03:55.001 away is a serious problem. 00:03:58.000 --> 00:04:02.000 The British government in the early 1700s 00:04:04.001 --> 00:04:10.001 earmarked a prize of, what was the amount then? 20,000 pounds, it's about $12 00:04:10.001 --> 00:04:17.001 million in today's currency to the first person who could come up with a way 00:04:18.000 --> 00:04:23.001 that ships could navigate safely to the equivalent of time of being able to keep 00:04:23.001 --> 00:04:28.000 time to an accuracy of about a minute after a long sea cruise. 00:04:29.001 --> 00:04:33.000 And for those of you who get turned on by navigation or clocks or 00:04:33.000 --> 00:04:35.000 anything else, really read this book. 00:04:35.000 --> 00:04:36.000 It's a fantastic book. 00:04:36.001 --> 00:04:38.001 I see a couple of people nodding yes, John do you agree? 00:04:39.000 --> 00:04:40.001 [...] sure if you finished it about a month ago, that's great. 00:04:43.000 --> 00:04:49.000 It's, I mean this was as good as Tom Clancy's idea that you can't put it down 00:04:49.000 --> 00:04:50.001 and you read until three o'clock in the morning. 00:04:51.000 --> 00:04:56.000 I want to discuss this whole thing on navigation by going back to the 1700s and 00:04:56.000 --> 00:05:00.001 showing a modern vintage 1700 APRS math. 00:05:05.000 --> 00:05:07.001 Because it illustrates a very interesting point. 00:05:08.000 --> 00:05:14.000 If you look at the map very critically, all of the features of, for instance, the 00:05:14.000 --> 00:05:17.000 New World were corrected in their locations North South. 00:05:18.000 --> 00:05:21.000 For instance, they knew where the mouth of the Amazon was. 00:05:22.000 --> 00:05:25.001 They knew the North South location of the bulge in Brazil. 00:05:26.000 --> 00:05:31.001 They knew the relative North South locations of all of the Caribbean islands with 00:05:31.001 --> 00:05:33.001 respect to Florida and the Keys. 00:05:34.000 --> 00:05:36.000 They knew where Chesapeake Bay was. 00:05:36.000 --> 00:05:40.001 They kind of missed a little bit out in the California area because they started 00:05:40.001 --> 00:05:46.001 sailing up the Gulf of California and found that it went a long 00:05:46.001 --> 00:05:48.001 ways and they didn't sail too far. 00:05:49.000 --> 00:05:52.001 And then they got up to the San Francisco area and started sailing South and 00:05:52.001 --> 00:05:55.000 found this big bay there and they thought the two were connected. 00:05:55.001 --> 00:05:58.001 That won't happen until the San Andreas Fault splits. 00:06:03.000 --> 00:06:05.000 They got the North South features right. 00:06:05.000 --> 00:06:07.000 They completely blew it East West. 00:06:07.001 --> 00:06:12.000 You can see that by looking at the shape of Africa, by looking at the width of 00:06:12.000 --> 00:06:19.000 India, by looking at where is Cape Town with respect 00:06:19.000 --> 00:06:22.001 to Italy in terms of our modern maps. 00:06:22.001 --> 00:06:24.000 They blew it East West. 00:06:24.000 --> 00:06:25.000 They got it North South. 00:06:25.000 --> 00:06:25.001 Why is that? 00:06:26.000 --> 00:06:31.000 With North South, you can measure your latitude when you're at sea with a 00:06:31.000 --> 00:06:33.000 relatively simple technique. 00:06:33.000 --> 00:06:38.000 You at least know what day it is and you can watch the sun from sunrise to sunset 00:06:38.000 --> 00:06:41.000 and find out what elevation does it get to at its highest angle. 00:06:42.001 --> 00:06:47.001 That and a simple essentially calendar tells you your latitude very accurately. 00:06:47.001 --> 00:06:49.001 You don't need any more information. 00:06:50.000 --> 00:06:55.000 The problem is that your East West location depends on having a precise time for 00:06:55.000 --> 00:07:00.000 sunrise or noon or some other external effect. 00:07:00.001 --> 00:07:06.001 And all of these East West errors that you see so evident on this map came 00:07:06.001 --> 00:07:11.000 because the mariners that were out there sailing around all of these 00:07:11.000 --> 00:07:12.001 places didn't know what time it was. 00:07:14.001 --> 00:07:21.001 So you look at a map like this and you see this absolutely critical relation 00:07:21.001 --> 00:07:27.000 of timing and navigation positions. 00:07:28.001 --> 00:07:30.001 And that's still there today. 00:07:31.001 --> 00:07:37.001 What we're gonna be talking about is systems where we measure, where we're 00:07:37.001 --> 00:07:40.001 located by using some timing information. 00:07:41.000 --> 00:07:47.000 Here is, unfortunately it's not the best view graph in the world but that's okay. 00:07:50.000 --> 00:07:52.001 Wanna give you a thought experiment. 00:07:53.000 --> 00:07:54.000 You've all done it. 00:07:54.000 --> 00:07:55.000 The lightning hits. 00:07:56.000 --> 00:07:57.000 You see the flash. 00:07:57.001 --> 00:07:58.001 You start counting seconds. 00:07:58.001 --> 00:08:00.000 How far are you away? 00:08:00.000 --> 00:08:04.001 You're a thousand feet per second away from it because the speed of sound is a 00:08:04.001 --> 00:08:09.000 thousand feet per second or about 300 meters per second. 00:08:09.000 --> 00:08:13.001 Now I'm gonna be in a lot of cases using metric measurements here. 00:08:13.001 --> 00:08:18.001 For those of you who, since I come from the Washington area, we have to be 00:08:18.001 --> 00:08:20.001 completely politically correct. 00:08:22.000 --> 00:08:28.000 And so we don't say, folks in the US don't know anything 00:08:28.000 --> 00:08:29.001 about the metric system. 00:08:30.000 --> 00:08:31.000 We're metric challenged. 00:08:32.000 --> 00:08:37.001 So for those of you who are metric challenged, a meter is a yard 00:08:37.001 --> 00:08:39.000 within about 10%. 00:08:40.000 --> 00:08:42.001 And a kilometer is a short mile. 00:08:43.001 --> 00:08:45.001 That sort of gets you in the right ballpark. 00:08:46.000 --> 00:08:50.000 I mean you're within factors of two or something when I say those things. 00:08:50.001 --> 00:08:54.001 Actually the meter equals a yard is correct or within 00:08:54.001 --> 00:08:56.000 10% so that's not a bad one. 00:08:58.000 --> 00:09:02.000 I found this, I have to tell a humorous story about myself here. 00:09:04.000 --> 00:09:05.001 Maybe you know I'm a radio astronomer. 00:09:06.000 --> 00:09:07.000 I'm a professional scientist. 00:09:07.001 --> 00:09:10.001 I remember a case in the early 1970s. 00:09:10.001 --> 00:09:16.001 I was in Sweden doing an experiment and we were using a radio telescope in Sweden 00:09:17.001 --> 00:09:24.000 and it's right on the sea coast and there was a storm coming in and I was left to 00:09:24.000 --> 00:09:31.000 run the telescope late at night and the people at the station told me, 00:09:31.000 --> 00:09:35.001 be sure to stow the telescope if the wind speed gets to be 25 meters per second. 00:09:36.001 --> 00:09:40.000 And it took me about three minutes of scratching to figure out whether 00:09:40.000 --> 00:09:41.001 that was a hard wind or a soft wind. 00:09:42.000 --> 00:09:43.001 I was metric challenged. 00:09:43.001 --> 00:09:50.001 I grew up with this antique system of units and the final conversion factor that 00:09:50.001 --> 00:09:54.000 clicked in my mind that made it so I could say, oh yeah, I know what that means 00:09:54.000 --> 00:09:59.000 was to think 60 miles an hour is 88 feet per second. 00:09:59.000 --> 00:10:00.001 I learned that in high school, algebra. 00:10:01.001 --> 00:10:06.000 And I could convert the feet to meters and that says, yeah, 00:10:06.000 --> 00:10:07.001 that's about a 50 mile an hour wind. 00:10:07.001 --> 00:10:10.001 That's when the wind, you know, I go outside and feel the wind getting 00:10:10.001 --> 00:10:12.000 to be high. 00:10:12.001 --> 00:10:17.001 Well, that came during the middle of an experiment where we were measuring some 00:10:17.001 --> 00:10:24.000 of the hydroxyl measures out in our galaxy and we were having 00:10:24.000 --> 00:10:27.000 to set the radial velocities in meters per second. 00:10:28.000 --> 00:10:32.000 So in my scientific world, I could think in terms of what frequency we had to set 00:10:32.000 --> 00:10:34.001 local oscillators to be able to receive this. 00:10:34.001 --> 00:10:39.001 But in terms of my physical realization, I had the problem of relating 25 meters 00:10:39.001 --> 00:10:41.001 per second into a hard wind versus a soft wind. 00:10:42.000 --> 00:10:45.000 We are metric challenged in this country and 00:10:45.000 --> 00:10:46.001 that's something that we gotta do something about. 00:10:47.001 --> 00:10:50.000 Okay, here's the Gennonkin experiment, thought experiment 00:10:50.000 --> 00:10:52.000 that I'm gonna suggest to you. 00:10:52.001 --> 00:10:53.001 The lightning hits. 00:10:54.000 --> 00:10:57.000 You're sitting there on two meters with your HT. 00:10:57.001 --> 00:10:59.001 Your names are Fred and Joe. 00:11:01.000 --> 00:11:07.000 And you're talking to two meters and you say, gee, that was a close one. 00:11:08.000 --> 00:11:13.000 I measured that as 4. 5 seconds, 4,500 feet away. 00:11:14.000 --> 00:11:16.000 And Joe says, gee, I did the same experiment. 00:11:17.000 --> 00:11:19.001 I measured it as about 5.7 seconds. 00:11:20.001 --> 00:11:25.001 Knowing where Fred lives and where Joe lives, we can then immediately know that 00:11:25.001 --> 00:11:28.000 there are only two places in the universe 00:11:28.000 --> 00:11:30.000 that that lightning crash could have hit. 00:11:30.001 --> 00:11:31.001 That's here and here. 00:11:32.000 --> 00:11:39.000 And because Fred happened to see the lightning crash out of his 00:11:39.000 --> 00:11:43.000 window and it was on the north side of the building, he knew that it had to be 00:11:43.000 --> 00:11:45.001 the north versus the south, one of those ambiguities. 00:11:46.000 --> 00:11:47.000 Now what did he make use of? 00:11:47.001 --> 00:11:53.000 Well, the timing signal, the event that started this was seeing the flash. 00:11:53.001 --> 00:11:59.001 The speed of light that conveyed the flash happening came to us at a speed of 300 00:11:59.001 --> 00:12:06.000 meters per microsecond, 1,000 feet per microsecond, one foot 00:12:06.000 --> 00:12:10.001 per nanosecond, for those of us who are metrically challenged, 00:12:10.001 --> 00:12:12.001 that's a nanosecond right there. 00:12:12.001 --> 00:12:17.000 I can remember Grace Hopper coming around and handing out nanosecond pieces of 00:12:17.000 --> 00:12:20.000 wire when she was talking about the HealthOS computers ran. 00:12:22.001 --> 00:12:25.001 So the speed of light compared to the speed of 00:12:25.001 --> 00:12:27.000 sound differ by a factor of a million. 00:12:28.000 --> 00:12:31.001 For those of you who are at Mike Japonas' talk, that's 10 to the sixth. 00:12:34.001 --> 00:12:39.001 At any rate, that is essentially instantaneous with respect to the 00:12:39.001 --> 00:12:41.000 sound velocity. 00:12:42.000 --> 00:12:46.001 So we actually had, in coming up with Fred and Joe being able to locate the 00:12:46.001 --> 00:12:49.001 lightning crash on the map, we had three pieces of information. 00:12:50.000 --> 00:12:56.001 We had a precise timing event that was perceived by our eye because it came at 00:12:56.001 --> 00:13:01.000 the speed of light, plus the two pieces of sound travel speed information. 00:13:01.001 --> 00:13:04.001 That was enough for us to be able to solve for the position. 00:13:06.000 --> 00:13:09.001 Now we could have turned that problem around and had both of these guys being 00:13:09.001 --> 00:13:16.001 transmitters and having the receiver be at that location and locate the position 00:13:16.001 --> 00:13:21.001 of the receiver, providing we have something that can measure both of the times. 00:13:22.000 --> 00:13:25.000 Otherwise, we can only measure the difference in arrival time. 00:13:26.000 --> 00:13:27.000 That's how the LAN works. 00:13:27.000 --> 00:13:34.000 Laran has a master transmitter that sits there at a frequency 00:13:34.000 --> 00:13:40.001 of about 100 kilohertz, transmitting a waveform that's about 10 pulses per second 00:13:40.001 --> 00:13:43.001 and you hear the master, then you hear the first 00:13:43.001 --> 00:13:45.000 slave and you measure that time interval. 00:13:46.000 --> 00:13:50.000 And you had the master and you hear the second slave and you measure that time 00:13:50.000 --> 00:13:55.000 interval and that sets up this kind of geometry here that allows you to locate 00:13:55.000 --> 00:13:58.000 where you are in a two dimensional flat world sense. 00:13:59.001 --> 00:14:04.001 Laran was the best navigation system that we had around up until 00:14:04.001 --> 00:14:06.001 about 15 years ago. 00:14:09.000 --> 00:14:15.000 It's been replaced by GPS, but that same concept applies to GPS because 00:14:15.000 --> 00:14:19.000 the GPS satellites are just clocks. 00:14:20.000 --> 00:14:24.000 For the purpose of this discussion, they are just clocks. 00:14:24.001 --> 00:14:30.000 They contain on board a cesium and in the case of the newest satellites that are 00:14:30.000 --> 00:14:34.000 going up in order to make them cheaper, that is a rubidium, there's actually a 00:14:34.000 --> 00:14:37.001 backup rubidium frequency standard on all of the present satellites with 00:14:37.001 --> 00:14:43.001 stability, accuracies, goodness of clocks at the levels of part and 10 to the 12 00:14:43.001 --> 00:14:45.001 through a part and 10 to the 13th. 00:14:46.001 --> 00:14:50.001 And that standard happens to be running at a frequency of 10.23 megahertz. 00:14:52.001 --> 00:14:59.001 And some of the critical things in here are that the 154th harmonic of that 00:14:59.001 --> 00:15:02.000 is the frequency that we listen to with GPS. 00:15:03.001 --> 00:15:08.001 And the code that we're gonna use as the principle code that we use is at 1 00:15:08.001 --> 00:15:10.001 .023 megabits per second. 00:15:11.000 --> 00:15:16.000 We don't have to do very much high math to realize that that's a 7490 00:15:16.000 --> 00:15:18.000 divider between those two. 00:15:22.000 --> 00:15:28.000 The sequence that transmits the primary timing information is a spread spectrum 00:15:28.000 --> 00:15:34.001 sequence that's 1023 bits long, going at a rate of 1.023 megabits per second says 00:15:34.001 --> 00:15:37.000 that that comes out once per millisecond. 00:15:38.000 --> 00:15:41.000 And then there's some other things like a 50-bit per second 00:15:41.000 --> 00:15:43.000 message and some other things. 00:15:43.000 --> 00:15:49.000 And I wanna just point out here because it will be important that those clocks in 00:15:49.000 --> 00:15:56.000 orbit are steered from the ground by the 00:15:56.000 --> 00:15:59.000 master clock at the US Naval Observatory here in the Washington 00:15:59.000 --> 00:16:03.000 area, at Al Gore's house. 00:16:06.001 --> 00:16:09.000 And the Naval Observatory keeps these clocks running to 00:16:09.000 --> 00:16:10.001 about the 10 nanosecond level. 00:16:11.000 --> 00:16:17.000 Okay, let me translate that set of words into a block diagram. 00:16:18.000 --> 00:16:25.000 Here is a block diagram of everything that is important to the small 00:16:25.000 --> 00:16:28.001 GPS user that's on the GPS satellite. 00:16:28.001 --> 00:16:30.001 All of the rest of the stuff is irrelevant. 00:16:31.000 --> 00:16:32.001 There's a bunch of other fancy things. 00:16:33.000 --> 00:16:33.001 We don't care about them. 00:16:34.001 --> 00:16:38.001 There's the 10.23 megahertz cesium and rubidium frequency standard. 00:16:39.000 --> 00:16:43.001 We'll come back and we'll talk about that box a little bit later, but that 10.23 00:16:43.001 --> 00:16:49.001 megahertz signal gets multiplied by 154 to make an L-band carrier at 00:16:49.001 --> 00:16:51.001 1575.42 megahertz. 00:16:52.000 --> 00:16:57.001 It's divided by 10 to give something that's gonna be a clock at 1 00:16:57.001 --> 00:16:59.001 .023 megabits per second. 00:17:01.000 --> 00:17:04.001 There's a computer that's involved in this because we're gonna have to keep all 00:17:04.001 --> 00:17:07.001 these guys synchronized and everything else. 00:17:09.000 --> 00:17:13.000 And we'll talk about some of these things that are important on that in a minute. 00:17:13.001 --> 00:17:20.000 There's a 10. 23 bit long pseudorandom noise sequence that 00:17:20.000 --> 00:17:23.000 has been a one millisecond repeat cycle. 00:17:24.000 --> 00:17:28.000 And that's used as a direct sequence spread spectrum code on this transmitter. 00:17:28.001 --> 00:17:34.001 That's combined with a 50 bit per second message which are combined. 00:17:35.000 --> 00:17:38.001 They're both digital so we can either think of them as being added or multiplied. 00:17:39.000 --> 00:17:40.000 It doesn't make any difference. 00:17:40.000 --> 00:17:45.000 And a module two adder which is called an exclusive OR gate which is then you, 00:17:45.000 --> 00:17:50.000 the polarity of the output of that is then used to flip the phase of the L-band 00:17:50.000 --> 00:17:57.000 transmitter in a BPSK signal and for simplicity think 00:17:57.000 --> 00:17:58.001 of that just as a doubly balanced mixer. 00:17:59.000 --> 00:18:01.000 Many circuits for about $7. 00:18:02.000 --> 00:18:05.000 The output of the doubly balanced mixer, we don't worry 00:18:05.000 --> 00:18:06.001 about filters and stuff like that. 00:18:06.001 --> 00:18:12.000 The simple block diagram goes to a big humongous power amplifier and is 00:18:12.000 --> 00:18:16.001 transmitted on the downlink on the circularly polarized antenna. 00:18:19.001 --> 00:18:23.001 On here, let's just talk about the characteristics of the 00:18:23.001 --> 00:18:25.000 digital signals that are in here. 00:18:26.000 --> 00:18:31.001 The 1.023 megabit per second sequence is, as I said, 10.23 bits long. 00:18:32.000 --> 00:18:35.001 The code that is used is called the gold code. 00:18:36.000 --> 00:18:41.000 It's derived from two different pseudo random 00:18:43.001 --> 00:18:48.000 sequence generators, 10 stage shift registers that are hooked up to 00:18:48.000 --> 00:18:49.001 give a pseudo random pattern. 00:18:50.001 --> 00:18:54.001 There are two of them, one of them that are the same on every GPS satellite. 00:18:55.001 --> 00:18:58.001 One of those, different taps on one of those. 00:18:58.001 --> 00:19:05.000 You can go along the shift register and pick out 10 different phases of the code. 00:19:05.001 --> 00:19:11.001 On one of those, you take and tap at an arbitrary shift register and then you tap 00:19:11.001 --> 00:19:15.001 that same one at a different point in the arbitrary shift register. 00:19:16.000 --> 00:19:19.000 That gives you 10 combinations of code on the first one. 00:19:19.001 --> 00:19:21.000 Then you got nine choices on the second. 00:19:21.001 --> 00:19:24.000 But because those are combined in the exclusive OR gate, that 00:19:24.000 --> 00:19:26.000 says it's really only half of that. 00:19:26.000 --> 00:19:31.000 That is 45 possible codes that describe all the GPS satellites. 00:19:31.000 --> 00:19:36.001 So it's 10 possibilities times nine possibilities, but 00:19:36.001 --> 00:19:38.000 you can flip those and they're the same. 00:19:38.000 --> 00:19:39.001 That means 45 possibilities. 00:19:40.001 --> 00:19:47.001 The GPS designers, the DOD folks in their infinite system picked 32 of 00:19:47.001 --> 00:19:53.000 those 45 codes and said, we will use these for all satellites in orbit. 00:19:54.001 --> 00:20:00.000 We will reserve another five of the codes for special purpose things. 00:20:00.000 --> 00:20:03.001 Things like pseudo lights and test transmitters and other fancy things. 00:20:04.000 --> 00:20:05.001 So that gets us up to 37. 00:20:07.000 --> 00:20:09.001 And they never talk about the other eight, but they're there. 00:20:11.001 --> 00:20:18.000 So they're really in fact 45 legal, all different codes that can be used 00:20:18.000 --> 00:20:22.000 and they only take selecting different taps on the shift register in order to be 00:20:22.000 --> 00:20:23.001 able to generate one versus the other. 00:20:24.001 --> 00:20:31.001 It's possible for you with about three ICs, maybe four to 00:20:31.001 --> 00:20:34.000 build a gold code generator. 00:20:34.001 --> 00:20:38.001 And if you have a 10 megahertz, a one megahertz clock, you can make 00:20:38.001 --> 00:20:40.000 your own GPS code generator. 00:20:40.000 --> 00:20:41.000 It's pretty simple. 00:20:44.000 --> 00:20:49.000 That code generator, every 20 cycles of that code generator, the 00:20:49.000 --> 00:20:50.001 phase may get flipped. 00:20:51.000 --> 00:20:52.001 Gotta realize this is just a phase flipper. 00:20:53.000 --> 00:20:54.000 It's an exclusive OR gate. 00:20:54.000 --> 00:21:00.000 And it's flipped by the data that comes out in something that's called the 00:21:00.000 --> 00:21:07.000 navigation message. 50 bits per second, that's 10.23, 1.023 megabits 00:21:07.000 --> 00:21:13.000 per second divided by 20460. 50 bit per second message, the 00:21:13.000 --> 00:21:14.001 message is 30 seconds long. 00:21:15.000 --> 00:21:16.001 That means 1500 bits. 00:21:17.001 --> 00:21:23.000 So in a sense, if you wanna think of this as a spread spectrum transmitter, it's 00:21:23.000 --> 00:21:26.001 a 50 bit per second message transmitter, is what the GPS is. 00:21:27.000 --> 00:21:33.000 But we're gonna make use of both the individual spreading code cycle 00:21:33.000 --> 00:21:35.000 clock as well as the data. 00:21:36.001 --> 00:21:40.000 So this is what the GPS satellite has in orbit. 00:21:40.000 --> 00:21:41.000 Pretty simple box. 00:21:41.001 --> 00:21:45.001 The up-light commands from the ground controllers are used to build 00:21:45.001 --> 00:21:47.000 things that go into that message. 00:21:49.000 --> 00:21:54.001 And we'll come back and talk in a little bit about what the SA phase didler does. 00:21:56.000 --> 00:21:58.000 Let me talk about the other side of it. 00:21:58.000 --> 00:21:59.001 What's in the GPS receiver? 00:22:01.000 --> 00:22:05.001 This is a generic block diagram of the receiver that's in one of these. 00:22:07.000 --> 00:22:12.000 It's the receiver that we're using in the TACs. 00:22:12.000 --> 00:22:14.000 It's every GPS receiver. 00:22:14.000 --> 00:22:19.000 First of all, there's a part of this that's analog that always scares people who 00:22:19.000 --> 00:22:26.000 tend to be digitally oriented, but it consists of an L band antenna, a low 00:22:26.000 --> 00:22:32.000 noise amplifier, also contained on this, a down converter mixer that comes off of 00:22:32.000 --> 00:22:36.000 a local oscillator that's got a fairly good crystal oscillator, goes through some 00:22:36.000 --> 00:22:39.001 set of IF stages and gets converted into a digital signal. 00:22:42.000 --> 00:22:47.000 We could have a long discussion, but it's quite adequate to simply have your 00:22:47.000 --> 00:22:49.000 analog to digital converter be a clipper. 00:22:49.000 --> 00:22:53.001 That is say, is the instantaneous polarity of the signal up or down? 00:22:55.001 --> 00:23:00.001 Some receivers, to get a little bit more sensitivity, use a two-bit sampler. 00:23:00.001 --> 00:23:04.000 I don't know of any GPS receivers out there that have more than two-bit 00:23:04.000 --> 00:23:06.000 samplers in their A to D converters. 00:23:06.000 --> 00:23:08.000 And this is directly sampling the IF. 00:23:09.000 --> 00:23:11.000 Now, what do we have to do to detect this? 00:23:11.001 --> 00:23:13.001 Well, let's give this some thought. 00:23:14.001 --> 00:23:17.000 The signal comes down from the GPS satellite. 00:23:17.001 --> 00:23:21.000 We don't know how far away the satellite is, so we don't know the code phase. 00:23:21.001 --> 00:23:26.000 So we're gonna have to somehow sit there and tune in code phase space in 00:23:26.000 --> 00:23:27.001 order to be able to extract the signal. 00:23:28.000 --> 00:23:30.000 But also, the satellite has a doppler shift. 00:23:30.001 --> 00:23:34.000 The signal from the satellite has a doppler shift, and in fact, also our first 00:23:34.000 --> 00:23:36.001 local oscillator may be at the wrong frequency. 00:23:36.001 --> 00:23:41.000 So we're gonna have to detect simultaneously in the frequency domain. 00:23:42.000 --> 00:23:46.001 We can generate a signal on the ground that matches the signal coming down from 00:23:46.001 --> 00:23:51.001 the GPS satellite, providing we can tune in two dimensions, time and 00:23:51.001 --> 00:23:53.000 frequency in terms of the code. 00:23:53.000 --> 00:23:55.000 Then we can generate our own replica. 00:23:56.000 --> 00:23:59.000 Then we can lock our replica on the incoming signal. 00:24:04.000 --> 00:24:08.001 And it's gonna be the parameters of that locking loop that are really the things 00:24:08.001 --> 00:24:11.000 that we use to extract all of the navigation data. 00:24:11.000 --> 00:24:17.000 That's typically done with essentially the schematic diagram that I show up here. 00:24:18.000 --> 00:24:20.001 The digital correlators are again exclusive OR gates. 00:24:20.001 --> 00:24:21.001 They multiply the signal. 00:24:22.001 --> 00:24:29.000 We end up with a two phase code generator that is making a replica of the 00:24:29.000 --> 00:24:36.000 code, and a two phase carrier oscillator, the two phases here are typically 00:24:36.000 --> 00:24:37.001 called prompt and early. 00:24:37.001 --> 00:24:41.000 They differ by one, or in some cases, not quite one, 00:24:41.000 --> 00:24:42.001 but a number similar to one bit. 00:24:45.000 --> 00:24:50.001 And in the frequency domain for the last local oscillator in the receiver, 00:24:51.000 --> 00:24:53.000 there's an in phase and a quadrature phase component. 00:24:54.000 --> 00:24:56.001 So we form all four possible products of those. 00:24:57.001 --> 00:25:03.000 Here in heavy lines, I formed one of them, which is the prompt bit of the code 00:25:03.001 --> 00:25:08.001 times the in phase bit of the oscillator, which I accumulate. 00:25:09.000 --> 00:25:10.000 This is just a counter. 00:25:11.000 --> 00:25:16.001 I count the number of times that these signals match versus the number of times 00:25:16.001 --> 00:25:22.001 that they don't match in a given period, and that can be done by just counting 00:25:22.001 --> 00:25:27.000 the number of ones that come out of that exclusive OR gate that occur 00:25:27.000 --> 00:25:28.001 during a given period of time. 00:25:29.001 --> 00:25:33.000 If the signals are perfectly correlated, they're either gonna match perfectly, so 00:25:33.000 --> 00:25:37.000 I'm gonna get all ones, or I'm gonna get all zeros because they 00:25:37.000 --> 00:25:38.001 match if they just happen to be out of phase. 00:25:39.000 --> 00:25:44.000 So all ones in that accumulator, or all zeros, means strong correlation. 00:25:44.001 --> 00:25:49.000 A number like a half of that in between says just noise. 00:25:50.001 --> 00:25:56.000 So I extract these four quadrature signals, quadrature in code and quadrature in 00:25:56.000 --> 00:26:01.000 local oscillator, and feed them down into something that's in essence a double 00:26:01.000 --> 00:26:04.000 digital signal processing costas loop. 00:26:06.000 --> 00:26:11.000 And use that to steer the phase and frequency of two numerically controlled 00:26:11.000 --> 00:26:13.000 oscillators, one that's generating the 00:26:13.000 --> 00:26:15.000 code, and one that's generating the carrier. 00:26:16.001 --> 00:26:21.000 Now, that costas loop is typically implemented in a microprocessor, but I show it 00:26:21.000 --> 00:26:27.001 here as a separate loop just for keeping in mind that it really is a digital way 00:26:27.001 --> 00:26:30.000 of making something that's sort of an analog process. 00:26:31.000 --> 00:26:38.000 The things like the carrier phase that's necessary to get 00:26:38.000 --> 00:26:44.000 the code match, the carrier phase necessary to get the carrier phase match, the 00:26:44.000 --> 00:26:50.001 polarity that comes out of the costas loop, the data polarity has in 00:26:50.001 --> 00:26:55.000 it that 50-bit per second message that we're gonna wanna decode. 00:26:55.001 --> 00:26:59.000 There's gonna be things like signal to noise ratio because on receivers like 00:26:59.000 --> 00:27:03.001 this, they got these neat little S-meter bars on it to tell how 00:27:03.001 --> 00:27:05.001 strong the signal is. 00:27:08.001 --> 00:27:11.001 So that somehow is intimately linked to a computer. 00:27:16.000 --> 00:27:19.000 The computer is running as a real-time computer. 00:27:20.000 --> 00:27:24.000 It's driven from the same clock that's controlling all of these other operations. 00:27:26.000 --> 00:27:30.001 And so I sort of show that link over here that that clock is probably derived 00:27:30.001 --> 00:27:32.001 from the same oscillator we see up here. 00:27:32.001 --> 00:27:36.001 So there's a timing clock as well as a frequency standard associated with that. 00:27:37.000 --> 00:27:41.000 And that real-time computer then after it gets all of this information and 00:27:41.000 --> 00:27:45.000 munches on it, talk a little in a minute about what munching it has to do, 00:27:45.000 --> 00:27:51.001 extracts the navigation data from the navigation message, performs 00:27:51.001 --> 00:27:55.001 PBT, that's position, velocity and time solution. 00:27:56.000 --> 00:27:58.000 We'll see why that's necessary in a minute. 00:27:58.001 --> 00:28:03.000 Displays the data to the user, talks to the outside world and whatever else it 00:28:03.000 --> 00:28:09.000 wants to do that is the place where the GPS receiver 00:28:09.000 --> 00:28:12.000 manufacturers put all their fancy whiz bang features. 00:28:12.000 --> 00:28:14.001 Does this drive an FCD panel, for instance? 00:28:14.001 --> 00:28:15.000 It may. 00:28:17.000 --> 00:28:22.001 And in the case of some of these receivers, which are important to us for one of 00:28:22.001 --> 00:28:27.000 the TAPR activities, that system timing clock may essentially have an output that 00:28:27.000 --> 00:28:29.000 is a one pulse per second signal. 00:28:30.000 --> 00:28:36.001 Now, let me, so that's what the 00:28:36.001 --> 00:28:38.001 transmitter and the receiver look like. 00:28:40.000 --> 00:28:45.000 Let me use a couple of word charts and then I'm gonna come back to the pictures. 00:28:46.000 --> 00:28:50.000 The way in which we do things with GPS, let's say we wanna find out where we're 00:28:50.000 --> 00:28:51.001 located and how fast we're moving. 00:28:52.001 --> 00:28:58.001 We measure the timing of several satellites 00:28:59.000 --> 00:29:02.000 with respect to our local internal clock. 00:29:03.001 --> 00:29:08.000 Our local clock's wrong in these cheap receivers, but at least we use the 00:29:08.000 --> 00:29:09.001 same clock for all of them. 00:29:11.001 --> 00:29:18.001 And the word that's usually used for that time difference 00:29:18.001 --> 00:29:24.001 between the satellite time that it's transmitting and what we perceive 00:29:24.001 --> 00:29:26.000 on the ground is called the pseudo range. 00:29:26.001 --> 00:29:30.001 It would actually be the range to the satellite if our local clock was set. 00:29:31.000 --> 00:29:34.001 Pseudo means not quite and the not quite is that 00:29:34.001 --> 00:29:36.000 our clock on the ground isn't perfect. 00:29:37.001 --> 00:29:43.001 If we take pseudo ranges to four satellites, that is a pair at times of four 00:29:43.001 --> 00:29:47.001 satellites and we know where the satellites are located. 00:29:48.000 --> 00:29:51.000 Now, the where are they located is transmitted to us as 00:29:51.000 --> 00:29:52.001 a part of this navigation message. 00:29:53.000 --> 00:29:56.000 Transmits down high accuracy Keplerian elements. 00:29:56.001 --> 00:30:02.000 We could use those four parameters to determine four parameters that apply to us. 00:30:02.000 --> 00:30:07.000 That is where we located in three dimensions, latitude, longitude, height, XYZ, 00:30:07.001 --> 00:30:11.000 or whatever other coordinates you wanna have, grid squares. 00:30:12.001 --> 00:30:17.001 And the fourth parameter is the error that's in your local timing clock that's 00:30:17.001 --> 00:30:19.000 inside the GPS receiver. 00:30:20.000 --> 00:30:23.001 If you're just navigating your boat, you really don't care about the timing 00:30:23.001 --> 00:30:28.000 error, so your receiver buries that down on screen number seven as to what time 00:30:28.000 --> 00:30:32.000 it is and doesn't tell you very much about it, but it had to solve for 00:30:32.000 --> 00:30:33.001 it in order to be able to make use of this. 00:30:33.001 --> 00:30:39.000 If you only wanted to do a two dimensional position, you're out on the ocean, you 00:30:39.000 --> 00:30:45.000 know your height because you know that mean sea level is determined more 00:30:45.000 --> 00:30:49.000 precisely even though there are waves and that kind of stuff. 00:30:49.000 --> 00:30:52.000 You know mean sea level more precisely than GPS is gonna 00:30:52.000 --> 00:30:53.001 find mean sea level for you. 00:30:53.001 --> 00:30:58.000 You only have to have three satellites because you only have to 00:30:58.000 --> 00:31:00.000 solve for your latitude and longitude. 00:31:00.000 --> 00:31:03.000 That's only two parameters and time being the third parameter. 00:31:05.000 --> 00:31:09.001 Also at the same time you make observations of the apparent frequency 00:31:09.001 --> 00:31:11.001 of the GPS satellites. 00:31:15.000 --> 00:31:20.001 Again, that apparent frequency is biased by things like the frequency error in 00:31:20.001 --> 00:31:23.000 the first local oscillator in your receiver. 00:31:24.000 --> 00:31:27.001 That's coming from the same thing that is the clock, so that's just 00:31:27.001 --> 00:31:29.001 how far off is the oscillator. 00:31:29.001 --> 00:31:34.001 So we call those pseudo range rates or apparent frequencies, 00:31:35.001 --> 00:31:37.000 apparent Doppler offsets. 00:31:38.000 --> 00:31:42.001 From that set of information, we can determine our three dimensional velocity, 00:31:43.001 --> 00:31:48.000 how fast are we moving and our local oscillator's frequency error. 00:31:51.001 --> 00:31:53.000 How well do we do that? 00:31:54.000 --> 00:31:59.000 Well, the signal that we're gonna finally use in the simple cheap dumb receivers, 00:31:59.000 --> 00:32:05.000 the Kmart receivers, is that CA code that stands for course acquisition. 00:32:05.000 --> 00:32:06.001 That's the 1023 bit code. 00:32:08.000 --> 00:32:14.000 And we can measure the code phase to a hundredth of a cycle if we're really good. 00:32:16.000 --> 00:32:19.000 Certainly a 30th of a cycle if we aren't very good. 00:32:19.000 --> 00:32:21.000 That's 10 degrees of electrical phase. 00:32:21.001 --> 00:32:26.001 Well, 3% of a microsecond is 30 nanoseconds. 00:32:26.001 --> 00:32:30.001 In time domain, which is 30 feet, which is 10 meters. 00:32:31.001 --> 00:32:33.000 And it may not be quite that good. 00:32:33.000 --> 00:32:38.001 I'll discuss PDOP in a minute, but sort of the 10 to 20 meters is how well can we 00:32:38.001 --> 00:32:40.001 measure each one of those guys typically. 00:32:43.000 --> 00:32:46.000 Now, let me continue this. 00:32:47.000 --> 00:32:53.001 So your GPS measure is the phase of that code to a fraction of the microsecond 00:32:54.000 --> 00:32:56.000 with respect to its internal clocks. 00:32:57.000 --> 00:33:03.000 The message contained information like the Keplerian satellite elements and those 00:33:03.000 --> 00:33:06.000 happen to be accurate to about 20 meters. 00:33:06.001 --> 00:33:08.000 How do they get those in there? 00:33:08.000 --> 00:33:12.000 It's not that the GPS satellite determines the coordinates, the position, the 00:33:12.000 --> 00:33:13.001 ephemeris, the Keplerian elements. 00:33:14.001 --> 00:33:19.000 It's that the ground determines that by observing GPS satellites 00:33:19.000 --> 00:33:20.001 and uplicking the information. 00:33:22.001 --> 00:33:27.000 And there's also a whole bunch of other information in that GPS message. 00:33:27.001 --> 00:33:32.001 So the GPS satellites are clocks and you compare them with 00:33:32.001 --> 00:33:34.000 your local clock on the ground. 00:33:37.001 --> 00:33:39.000 Let's see, we already did that one. 00:33:39.000 --> 00:33:45.001 Now, I told you I was gonna be irreverent to the military. 00:33:46.000 --> 00:33:51.001 The military, the DOD unfortunately imposes selective availability. 00:33:53.000 --> 00:33:57.000 Now, I will now give you the definitive statement as to just 00:33:57.000 --> 00:33:59.000 what is selective availability. 00:34:00.000 --> 00:34:02.000 And I'm gonna get back to my block diagram. 00:34:03.000 --> 00:34:07.000 Here is the block diagram of the spacecraft. 00:34:09.000 --> 00:34:13.000 In the output of that frequency standard, there's a phase diddler. 00:34:13.001 --> 00:34:17.000 Think of this as just a line stretcher, a piece of 00:34:17.000 --> 00:34:18.001 transmission line that you can stretch. 00:34:19.001 --> 00:34:24.001 And up in the GPS satellites, the DOD, because they go for such 00:34:24.001 --> 00:34:26.001 things, has trained a mouse. 00:34:28.000 --> 00:34:33.000 And the mouse is instructed to sit there and continually change 00:34:33.000 --> 00:34:35.000 the length of this line stretcher. 00:34:35.001 --> 00:34:41.001 He sits there and does this all day long, moving the line stretcher in and out. 00:34:42.000 --> 00:34:45.001 He does this according to a preset pattern. 00:34:46.000 --> 00:34:49.000 And he is told only do it so fast. 00:34:49.001 --> 00:34:51.001 Don't make your strokes too fast. 00:34:52.001 --> 00:34:56.000 And you can only go so far because your arms are only that long. 00:34:59.001 --> 00:35:04.000 So that's what the DOD does, is that they have this trained mouse sitting up 00:35:04.000 --> 00:35:07.001 there in the spacecraft doing its thing. 00:35:10.000 --> 00:35:17.000 He does it under the control of the spacecraft computer and he does it with a 00:35:17.000 --> 00:35:23.001 magic code that only other DOD smart mice know to do 00:35:23.001 --> 00:35:28.001 because they sit there on the ground and do just exactly the opposite of what the 00:35:28.001 --> 00:35:30.001 mouse in the spacecraft is gonna do. 00:35:34.000 --> 00:35:37.000 That's what SA is, selective availability. 00:35:38.000 --> 00:35:42.000 The military takes a perfectly good system, really a 00:35:42.000 --> 00:35:43.001 nice system and screws it up. 00:35:44.001 --> 00:35:51.000 And they do this in order to make this, have this mystique that it is a system 00:35:51.000 --> 00:35:55.000 that the military owns and you guys that are down here on 00:35:55.000 --> 00:35:56.001 the ground, you better remember it. 00:35:57.001 --> 00:35:58.001 Now what's the effect of that? 00:35:58.001 --> 00:36:02.001 Well first of all, depending on how fast mouse is sitting there doing his thing, 00:36:03.001 --> 00:36:06.000 that affects the velocities you see on the ground. 00:36:06.001 --> 00:36:11.000 Everybody who has a GPS receiver on the ground, they pull up to the stop light, 00:36:11.000 --> 00:36:14.000 they stop their car and the receiver still says they're moving 00:36:14.000 --> 00:36:16.000 2.3 miles per hour. 00:36:17.000 --> 00:36:19.000 That says how fast is the mouse's stroke. 00:36:21.000 --> 00:36:27.000 We also know that if you sit there and run a GPS receiver at a fixed location for 00:36:27.000 --> 00:36:29.001 a while, you'll find that you end up with the 00:36:29.001 --> 00:36:31.000 position wandering all over the place. 00:36:31.001 --> 00:36:37.000 Typically the peak error is about 100 meters and that's what the DOD sort of 00:36:37.000 --> 00:36:42.000 guarantees that they're gonna do almost all the time, but occasionally not, but 00:36:42.000 --> 00:36:44.000 that's assuming that you're seeing plenty of satellites. 00:36:45.000 --> 00:36:48.001 If you don't see very many satellites, you get hit a little bit worse. 00:36:50.000 --> 00:36:56.000 This is one of the biggest annoyances of the GPS system has been the fact that 00:36:56.000 --> 00:37:02.001 this perfectly good system funded by the military, funded by our taxpayers 00:37:02.001 --> 00:37:07.000 money, sits there and intentionally screws it up for all of the rest of us who 00:37:07.000 --> 00:37:09.000 are sitting there just trying to use it parasitically. 00:37:12.000 --> 00:37:14.001 So that's what selective availability is. 00:37:15.000 --> 00:37:19.001 You can see that it doesn't make me happy. 00:37:20.000 --> 00:37:25.000 It turns out that much of the effort, because the military puts selective 00:37:25.000 --> 00:37:31.000 availability on the GPS satellites, this is actually made a bit of blessing in 00:37:31.000 --> 00:37:38.000 disguise because its effects on the user on the ground are really very annoying. 00:37:38.001 --> 00:37:41.001 You know you're not moving 2.3 miles an hour 00:37:41.001 --> 00:37:43.000 when you're stopped at the stoplight. 00:37:44.000 --> 00:37:45.000 How do we fix that? 00:37:45.001 --> 00:37:47.001 Well, there are a couple of things that we can do to fix it. 00:37:47.001 --> 00:37:51.001 One is that we can go out and try to hire our own mouse, but the DOD doesn't like 00:37:51.001 --> 00:37:54.001 us to do that and they really keep tight control for these keys. 00:37:57.000 --> 00:38:01.001 Or we could be a little bit smart about this and do one of two things. 00:38:02.000 --> 00:38:07.001 One, first thing we can do is that we become smart users. 00:38:09.001 --> 00:38:16.000 The smart user and the receiver manufacturers have realized that the guy who buys 00:38:16.000 --> 00:38:19.000 this to use it on his boat is not gonna be a very smart user. 00:38:19.001 --> 00:38:24.000 The smart user can say, ah, each one of the mice 00:38:24.000 --> 00:38:25.001 is doing his own thing differently. 00:38:26.000 --> 00:38:30.000 The more mice I observe, the more I can start beating this 00:38:30.000 --> 00:38:31.001 down, square root of NFX. 00:38:32.000 --> 00:38:34.001 I don't use just four satellites, I use a bunch. 00:38:35.001 --> 00:38:39.000 But right now, as we'll see in a little bit, the constellation of GPS satellites 00:38:39.000 --> 00:38:43.000 is such that you almost always have seven or eight visible. 00:38:44.000 --> 00:38:48.000 So we can be smart users, we can tell our receiver manufacturers 00:38:48.000 --> 00:38:50.000 make your receivers smarter. 00:38:51.000 --> 00:38:57.001 The newest version of the Garmin, the GPS 2 Plus, is a 12 channel parallel. 00:38:58.000 --> 00:39:01.001 It's got 12 of those costus loops running in it simultaneously. 00:39:02.001 --> 00:39:05.001 And it uses every satellite it can find in the sky. 00:39:07.000 --> 00:39:11.001 As opposed to some of the earlier receivers, brands that I won't mention, but 00:39:11.001 --> 00:39:18.000 their color was yellow and they sold for high prices and are depicted in lots of 00:39:18.000 --> 00:39:23.000 advertisements, said, oh, I only need four 00:39:23.000 --> 00:39:24.001 satellites to make my position solution. 00:39:25.001 --> 00:39:29.001 I, my receiver, will decide which of the best four satellites to use and I will 00:39:29.001 --> 00:39:31.000 use those even though I can see more. 00:39:33.000 --> 00:39:35.000 So the receiver technology's improved. 00:39:35.001 --> 00:39:41.000 We've got a lot more stuff in the box that you can buy for $250 at Kmart now than 00:39:41.000 --> 00:39:45.001 was in the box that you would buy from Mr. Tribble, I'm sorry, the yellow box 00:39:45.001 --> 00:39:51.001 that you would buy six or seven years ago for $1,000. 00:39:52.000 --> 00:39:54.001 They're much better receivers, that's helped. 00:39:56.000 --> 00:40:00.000 We could be smart users, improve this a little bit more. 00:40:01.001 --> 00:40:07.000 One of the things is that, let's take one of the really frequent users of GPS for 00:40:07.000 --> 00:40:09.000 navigation are the boat owners. 00:40:10.000 --> 00:40:14.001 It's really neat when the fog sets in and you're out on Chesapeake Bay to know 00:40:14.001 --> 00:40:17.000 how to get back to the harbor. 00:40:18.000 --> 00:40:21.001 And this technology is absolutely superb for them. 00:40:22.001 --> 00:40:26.001 Unfortunately, the receiver manufacturers haven't realized one of the important 00:40:26.001 --> 00:40:30.000 facts that the boat users have and that is that they know how high they are. 00:40:30.000 --> 00:40:35.000 And these receivers, most receivers do not let you say, I'm in my position, 00:40:35.001 --> 00:40:39.000 you're gonna be able to find it, don't solve for my high, just solve for my 00:40:39.000 --> 00:40:42.001 latitude and longitude, that is a two dimensional position fix. 00:40:43.001 --> 00:40:46.001 That's a failing, I think, that a lot of the manufacturers still have. 00:40:47.000 --> 00:40:51.000 We'll come back to another fix that the users can do in a minute, but I wanna 00:40:51.000 --> 00:40:57.000 discuss a little how we, in my picture 00:40:57.000 --> 00:41:03.001 of Fred and Joe and the lightning bolt, we sort of indicated that at the place 00:41:03.001 --> 00:41:06.001 where these two curves cross, that determines the position. 00:41:07.000 --> 00:41:08.000 Well, how well does it do that? 00:41:08.001 --> 00:41:10.001 Well, here's a blown up sketch. 00:41:11.000 --> 00:41:14.001 There's always a measurement error associated with any of these processes and I 00:41:14.001 --> 00:41:20.000 tried to show the measurement error as being the width of the blue, the aqua and 00:41:20.000 --> 00:41:26.000 the red traces here, some intrinsic measurement precision, having to do with 00:41:26.000 --> 00:41:30.000 noise, the laws of physics, how cheap the receiver is and a whole bunch of other 00:41:30.000 --> 00:41:33.001 things as well as how good is the signals coming from the satellite. 00:41:34.001 --> 00:41:38.000 Now, when the two signals that you're trying, the two paths that you're trying to 00:41:38.000 --> 00:41:45.000 follow, or trying to use intersect at a fairly flat angle, then the 00:41:45.000 --> 00:41:48.000 width of the intersection can be very wide. 00:41:49.001 --> 00:41:54.000 In the opposite direction, I show this just as X and Y coordinates here, 00:41:54.001 --> 00:41:56.000 it can be very narrow. 00:41:56.001 --> 00:41:59.001 That is, it's an oblong shaped intersection. 00:42:00.001 --> 00:42:06.000 In the dimension that's bad, our precision, our measurement precision has been 00:42:06.000 --> 00:42:09.000 diluted by the geometry. 00:42:10.000 --> 00:42:15.000 You'll see on every GPS receiver the words, DOP, something DOP, and that means 00:42:15.000 --> 00:42:17.000 dilution of precision. 00:42:17.001 --> 00:42:24.001 That's purely a geometric number that says, how much wider is this in a given 00:42:24.001 --> 00:42:28.001 coordinate than is the intrinsic properties of the receiver? 00:42:29.001 --> 00:42:35.000 Dilution of precision, so X-DOP in this case, since this is the X coordinate 00:42:35.000 --> 00:42:40.001 going that way, the X-DOP uncertainty is about four, where the Y-DOP 00:42:40.001 --> 00:42:43.000 is a factor of about one. 00:42:45.000 --> 00:42:52.000 Now, for the GPS systems, what we get in the way of DOPs 00:42:52.000 --> 00:42:54.001 is dependent on how many satellites are visible. 00:42:54.001 --> 00:42:58.001 This is for, I think it was two days ago that I made the plot, it shows the 00:42:58.001 --> 00:43:02.000 number of satellites that are visible over a 24 hour 00:43:02.000 --> 00:43:04.001 period in Eastern Standard Time. 00:43:04.001 --> 00:43:09.000 For here in the Washington area, it actually is at my location, which is about 00:43:09.000 --> 00:43:10.001 20 kilometers from this location. 00:43:10.001 --> 00:43:16.000 That's about 15 or so miles for the metrically challenged. 00:43:17.001 --> 00:43:23.000 The number of satellites that's visible at any given time ranges from a low of 00:43:23.000 --> 00:43:27.000 four at slightly after 9 a.m. 00:43:27.001 --> 00:43:33.000 It's just about right now, up to a high of eight, if I can see 00:43:33.000 --> 00:43:34.001 the 15 degrees elevation. 00:43:35.001 --> 00:43:37.001 If I see lower, I'll see more satellites. 00:43:38.001 --> 00:43:42.001 That's out of a total constellation right now of 25 00:43:42.001 --> 00:43:44.001 satellites that are available. 00:43:45.000 --> 00:43:52.000 Now, the effect of that is that for horizontal determinations, the horizontal DOP 00:43:52.000 --> 00:43:53.001 through the day looks like this. 00:43:53.001 --> 00:43:56.001 Pretty low, it's a number varying from one to two. 00:43:57.001 --> 00:44:03.000 If a perfect system was capable of a 10 meter measurement, this says we 00:44:03.000 --> 00:44:05.000 get about 20 meters in the horizontal. 00:44:06.000 --> 00:44:08.001 Very small, very low numbers. 00:44:09.000 --> 00:44:12.001 That's again, computed for the same 15 degree elevation, computed 00:44:12.001 --> 00:44:14.000 for the Washington area. 00:44:14.001 --> 00:44:17.000 The highest peak that you see there is that 00:44:17.000 --> 00:44:18.001 time, there were only four satellites available. 00:44:19.000 --> 00:44:20.000 That's the one right there. 00:44:21.000 --> 00:44:25.000 So, horizontal measurements are always very good. 00:44:26.001 --> 00:44:31.000 Part of the reason for that is that the GPS satellites are over the entire sky 00:44:31.000 --> 00:44:34.000 and you'll end up with some north of you and some south of you and some 00:44:34.000 --> 00:44:35.001 east of you and some west of you. 00:44:36.000 --> 00:44:39.000 So, it's basically, you end up with lots of intersecting lines. 00:44:41.001 --> 00:44:47.000 If you look at the vertical, the how high am I, it's a much worse case. 00:44:49.000 --> 00:44:55.001 The vertical DOP can range up to a peak of six or 00:44:55.001 --> 00:44:57.000 seven for the same case. 00:44:58.001 --> 00:45:02.000 That case really had four satellites available as this isolated 00:45:02.000 --> 00:45:03.001 little spike at that time. 00:45:04.001 --> 00:45:11.001 And late in the evening, from about 10 p. m. local time to about two a.m. local 00:45:11.001 --> 00:45:13.001 time, it's pretty bad in this area. 00:45:14.001 --> 00:45:17.000 During part of the day, it's as good as possible. 00:45:17.000 --> 00:45:20.000 Two, but there are times during the day it gets as bad as six. 00:45:21.000 --> 00:45:27.001 In general, the vertical DOP is about three times worse than the horizontal DOP 00:45:27.001 --> 00:45:31.001 as a rule of thumb, but there are times that it's even worse than that. 00:45:32.000 --> 00:45:36.000 Part of the reason is that for the horizontal DOP, I said we had satellites 00:45:36.000 --> 00:45:40.001 north, south, east, and west of us that help pin this down real well horizontally 00:45:40.001 --> 00:45:42.001 in two dimensions, you know, all dimensions. 00:45:43.001 --> 00:45:46.001 To pick out our vertical, we have satellites that maybe are straight overhead 00:45:46.001 --> 00:45:48.001 going down to the horizon. 00:45:48.001 --> 00:45:50.000 We don't have any below our feet. 00:45:51.000 --> 00:45:57.000 So we only have one hemisphere of space to be able to determine things. 00:45:57.000 --> 00:45:59.001 And it's the missing bottom hemisphere, the fact 00:45:59.001 --> 00:46:01.000 that the Earth is not transparent. 00:46:02.000 --> 00:46:04.001 That makes it, is the fundamental reason why 00:46:04.001 --> 00:46:06.000 the vertical measurements are always poor. 00:46:07.001 --> 00:46:13.001 Now, in your receivers, in the messages coming out, you'll see also a 00:46:13.001 --> 00:46:15.000 parameter called PDOP. 00:46:16.000 --> 00:46:22.000 Here's the PDOP, that's overall position, dilution of precision, which is the 00:46:22.000 --> 00:46:28.001 combination of vertical DOP, root sum squared with horizontal DOP. 00:46:32.000 --> 00:46:36.000 So the PDOP is always worse than either of the other two. 00:46:36.001 --> 00:46:40.001 And I would basically recommend people look at H-DOP and D-DOP because it 00:46:40.001 --> 00:46:42.001 tells you really what the components are. 00:46:44.001 --> 00:46:48.000 One way that we can improve that situation is by having more satellites. 00:46:49.000 --> 00:46:54.000 I don't say that this is very feasible right now, but we can do much better if we 00:46:54.000 --> 00:46:56.001 use the other 19 navigation satellites that are 00:46:56.001 --> 00:46:59.000 available, which are the GLONASS satellites. 00:47:00.000 --> 00:47:05.000 Same period of time, the minimum number of satellites is seven, or 00:47:05.000 --> 00:47:06.001 nine a.m. whole. 00:47:07.000 --> 00:47:12.000 We now have 12 satellites instead of four because the Russian satellites happen 00:47:12.000 --> 00:47:15.000 to be at just the right place, and we hit a maximum of 14. 00:47:16.001 --> 00:47:22.000 So a lot of the reason that people do better if they happen to have a combined 00:47:22.000 --> 00:47:26.000 GPS and GLONASS system is just that there's a lot more satellites available. 00:47:26.001 --> 00:47:29.000 You double, essentially double the number of satellites. 00:47:29.001 --> 00:47:35.000 So where we, before, had a peak of eight, we now get a peak of 14, where we had a 00:47:35.000 --> 00:47:37.001 low of four, we now have a low of about seven. 00:47:39.001 --> 00:47:43.001 That doesn't say the GLONASS system is easy to use, and it doesn't say that you 00:47:43.001 --> 00:47:45.001 have cheap K-Mart receivers. 00:47:47.001 --> 00:47:52.001 Now let me talk about high accuracy GPS for a bit. 00:47:53.001 --> 00:47:56.000 I want to do this by predicating this with 00:47:56.000 --> 00:47:58.000 some comments about what I do for a living. 00:47:58.001 --> 00:48:00.000 I work for NASA. 00:48:01.000 --> 00:48:04.001 I direct a program at NASA called Very Long Baseline Interferometry. 00:48:04.001 --> 00:48:10.000 We use radio telescopes like this all around the world to make extremely high 00:48:10.000 --> 00:48:15.000 accuracy measurements of where these telescopes are located, how fast is the 00:48:15.000 --> 00:48:17.000 Earth spinning, how's it wobbling, and so forth. 00:48:19.001 --> 00:48:25.000 The accuracies we achieve on the better of our systems are down at levels of 00:48:25.000 --> 00:48:30.000 about three millimeters for 24 hours of observation and baselines that are 00:48:30.000 --> 00:48:32.001 six or seven thousand kilometers. 00:48:33.000 --> 00:48:39.001 Just to put that in context for the metrically challenged, the other unit that we 00:48:39.001 --> 00:48:43.000 talk about here is in the resolution and angle sense. 00:48:43.000 --> 00:48:49.001 You achieve angular accuracies of the order of a tenth or a 00:48:49.001 --> 00:48:51.001 20th of a milliarc second. 00:48:52.001 --> 00:48:59.000 A milliarc second, one milliarc second, is basically 00:48:59.000 --> 00:49:04.000 two centimeters, seen at 4,000 kilometers. 00:49:04.001 --> 00:49:09.000 The size of a quarter held over San Francisco is seen from here. 00:49:10.000 --> 00:49:16.000 The tenth or 20th that says that you can actually see George Washington's eye 00:49:16.000 --> 00:49:21.000 sockets on the quarter held over San Francisco viewed from here. 00:49:21.000 --> 00:49:24.001 With these techniques using these big radio telescopes, we can do that. 00:49:25.000 --> 00:49:30.001 This particular radio telescope is on the Big Island of Hawaii, that's one of the 00:49:30.001 --> 00:49:32.001 peaks, that's Mauna Kea in the background. 00:49:34.000 --> 00:49:39.000 This is a telescope that's operated by the National Radio Astronomy Observatory. 00:49:41.001 --> 00:49:46.000 I help coordinate the use of the, I'm really responsible for coordinating the use 00:49:46.000 --> 00:49:49.000 of these guys all around the world. 00:49:49.001 --> 00:49:54.000 Okay, we've been developing this technique for doing these high accuracy 00:49:54.000 --> 00:49:56.001 measurements over the last 20 or 25 years. 00:49:56.001 --> 00:49:59.001 The GPS people come along and say we can do almost as good and 00:49:59.001 --> 00:50:01.000 we can really do it a lot cheaper. 00:50:02.001 --> 00:50:07.000 And so a large part of my life has been trying to make sure I really understand 00:50:07.000 --> 00:50:10.001 how well GPS can do and to try to capitalize on the synergy 00:50:10.001 --> 00:50:12.000 of using the two systems together. 00:50:13.000 --> 00:50:20.000 In the high accuracy GPS world, I want to draw attention to this chart. 00:50:20.000 --> 00:50:22.001 This is pulled off of one of our web pages at Goddard. 00:50:22.001 --> 00:50:24.001 I'm sorry, it's slightly too wide to show. 00:50:26.000 --> 00:50:30.001 I want to point out that by post-processing the carrier phase data from dual 00:50:30.001 --> 00:50:35.001 frequency high accuracy receivers, surveyors and scientists routinely obtain 00:50:35.001 --> 00:50:39.000 results at the sub-centimeter level. 00:50:40.001 --> 00:50:45.001 Post-processing, that is you collect the data for a day, you somehow bring it 00:50:45.001 --> 00:50:49.001 back, you munch the data and you can get the centimeter level results. 00:50:50.001 --> 00:50:56.000 Dual frequency is to remove ionospheric biases and the GPS system actually has 00:50:56.000 --> 00:51:01.001 two down links, the L1 I described earlier and L2 which is at 1227 megahertz and 00:51:01.001 --> 00:51:03.001 yes there's been a lot of discussion about other 00:51:03.001 --> 00:51:05.001 frequencies, I won't go into that. 00:51:07.000 --> 00:51:11.001 The community around the world banded together to form an organization called the 00:51:11.001 --> 00:51:14.000 International GPS Service for Geodynamics. 00:51:16.000 --> 00:51:22.001 Data is logged in RINEX form transmitted by the internet from over 100 sites and 00:51:22.001 --> 00:51:26.000 results are typically available to the users within about 24 hours. 00:51:27.000 --> 00:51:33.001 Here's the map as of last week of these permanently 00:51:33.001 --> 00:51:39.001 operating tracking stations around the world that are contributing data that in 00:51:39.001 --> 00:51:43.001 general arrives within 24 hours although a few of them have some problems. 00:51:44.000 --> 00:51:48.001 It's still a little hard to get internet access to Krasnoyarsk reliably 00:51:48.001 --> 00:51:50.001 within 24 hours. 00:51:51.000 --> 00:51:56.001 Alma Ata and Bishtek in Kazakhstan and Kyrgyzstan are a little bit of a problem. 00:51:57.001 --> 00:52:03.000 Yerkutsk is a lot of problem getting data out and places like the Australian 00:52:03.000 --> 00:52:07.000 Davis and Casey sites in Antarctica it's a little problems getting the data out. 00:52:07.001 --> 00:52:10.001 But in general it's available within 24 hours, this 00:52:10.001 --> 00:52:12.001 is about 100 dots around the world. 00:52:12.001 --> 00:52:17.000 Ones that have little red dots in it are places that I've had some personal 00:52:17.000 --> 00:52:19.000 responsibility for making this network work. 00:52:19.001 --> 00:52:22.001 And you'll notice one of them is in Greenbelt just down the road here 00:52:22.001 --> 00:52:24.001 down the Baltimore, Washington, Parkway. 00:52:25.000 --> 00:52:27.000 I'll mention in a minute differential GPS. 00:52:27.001 --> 00:52:33.000 That Greenbelt line is the site of my differential GPS beacon that's on 145.79. 00:52:36.000 --> 00:52:40.001 The international service, the IGS, the International GPS Service for Geodynamics 00:52:40.001 --> 00:52:42.001 does scientific programs. 00:52:43.000 --> 00:52:46.001 It's all a collaborative effort, there's no big international money exchange, 00:52:46.001 --> 00:52:49.001 everything is funded by the local countries. 00:52:50.000 --> 00:52:54.001 But it gives global distribution for the data for programs like monitoring how 00:52:54.001 --> 00:52:58.000 the earth is deforming, how the earth spins and so forth. 00:52:58.000 --> 00:53:00.000 Things very similar to what I do with the very long 00:53:00.000 --> 00:53:01.001 baseline interferometry network. 00:53:03.000 --> 00:53:07.001 So it's justified by the science, international cooperative effort. 00:53:08.000 --> 00:53:12.001 If you want to see these web pages that I'm reproducing here it's cddisa 00:53:12.001 --> 00:53:15.000 .gsfc.nasa.gov. 00:53:18.000 --> 00:53:23.000 Second way that we beat selective availability and do better than we would have 00:53:23.000 --> 00:53:28.001 done under other conditions is by differential GPS. 00:53:29.000 --> 00:53:31.000 This is sort of going to be the last topic. 00:53:33.000 --> 00:53:39.001 Over here we have the typical user GPS receiver but to that we've added 00:53:39.001 --> 00:53:41.000 another element for the system. 00:53:42.000 --> 00:53:44.000 Here I'm showing it only observing four 00:53:44.000 --> 00:53:46.000 satellites, that's enough for the description. 00:53:46.001 --> 00:53:49.001 At some location we have a high quality GPS receiver. 00:53:50.000 --> 00:53:55.000 We know its location and we will tell the receiver what its 00:53:55.000 --> 00:53:56.001 location is, it's fixed. 00:53:57.001 --> 00:54:04.000 In the case of W3I-WI-13 it is the location of one of those hundred plus stations 00:54:04.000 --> 00:54:05.001 that was on the previous map. 00:54:07.000 --> 00:54:11.000 And it's running parasitically with a power splitter that's looking at the same 00:54:11.000 --> 00:54:14.000 antenna that provides data to that big network. 00:54:15.000 --> 00:54:20.001 Since the location is known, those pseudo ranges, delta T and the pseudo range 00:54:20.001 --> 00:54:26.000 rates, delta T dot for each of the satellites that are in view can be combined 00:54:26.000 --> 00:54:29.000 together and transmitted to some other user. 00:54:29.000 --> 00:54:31.000 They're combined together in a standard format. 00:54:32.000 --> 00:54:35.001 Most common format for this is called RTCM for Radio Technical 00:54:35.001 --> 00:54:37.000 Commission Maritime. 00:54:38.000 --> 00:54:44.001 SC104, subcommittee number 104, and a specification that they have set up that 00:54:44.001 --> 00:54:47.000 tells how will these bits be distributed. 00:54:48.000 --> 00:54:52.001 The actual message format is something that looks sort of like the GPS message 00:54:52.001 --> 00:54:58.000 format, which is a really bastard format to encode and decode, but 00:54:58.000 --> 00:54:59.001 at least it's been done many times. 00:55:00.000 --> 00:55:03.001 And that set of corrections are collected together and transmitted over some 00:55:03.001 --> 00:55:10.000 radio transmitter and the user has a second radio and applies those corrections 00:55:10.000 --> 00:55:14.000 directly to the observations, removing the errors. 00:55:15.000 --> 00:55:20.001 With differential GPS, that typical dumb, cheap receiver gets about one meter 00:55:20.001 --> 00:55:24.000 performance and the speed reads zero when you're stopped at the traffic light.